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The Dilation Coefficient of Complete Graphs

Boris Horvat ; IMFM, University of Ljubljana, Jadranska 19, Ljubljana, Slovenia
Tomaž Pisanski ; IMFM, University of Ljubljana, Jadranska 19, Ljubljana, and University of Primorska, Koper, Slovenia
Arjana Žitnik ; IMFM, University of Ljubljana, Jadranska 19, Ljubljana, Slovenia

Puni tekst: engleski, pdf (5 MB) str. 771-779 preuzimanja: 743* citiraj
APA 6th Edition
Horvat, B., Pisanski, T. i Žitnik, A. (2009). The Dilation Coefficient of Complete Graphs. Croatica Chemica Acta, 82 (4), 771-779. Preuzeto s https://hrcak.srce.hr/45617
MLA 8th Edition
Horvat, Boris, et al. "The Dilation Coefficient of Complete Graphs." Croatica Chemica Acta, vol. 82, br. 4, 2009, str. 771-779. https://hrcak.srce.hr/45617. Citirano 09.03.2021.
Chicago 17th Edition
Horvat, Boris, Tomaž Pisanski i Arjana Žitnik. "The Dilation Coefficient of Complete Graphs." Croatica Chemica Acta 82, br. 4 (2009): 771-779. https://hrcak.srce.hr/45617
Harvard
Horvat, B., Pisanski, T., i Žitnik, A. (2009). 'The Dilation Coefficient of Complete Graphs', Croatica Chemica Acta, 82(4), str. 771-779. Preuzeto s: https://hrcak.srce.hr/45617 (Datum pristupa: 09.03.2021.)
Vancouver
Horvat B, Pisanski T, Žitnik A. The Dilation Coefficient of Complete Graphs. Croatica Chemica Acta [Internet]. 2009 [pristupljeno 09.03.2021.];82(4):771-779. Dostupno na: https://hrcak.srce.hr/45617
IEEE
B. Horvat, T. Pisanski i A. Žitnik, "The Dilation Coefficient of Complete Graphs", Croatica Chemica Acta, vol.82, br. 4, str. 771-779, 2009. [Online]. Dostupno na: https://hrcak.srce.hr/45617. [Citirano: 09.03.2021.]

Sažetak

The dilation coefficient of a graph representation is defined as the quotient of the longest and the shortest edge representation. The minimum of the dilation coefficients over all planar representations of a graph G is called the dilation coefficient of the graph G. The dilation coefficient of different planar representations of complete graphs is considered and upper and lower bounds for the dilation coefficients of complete graphs are given. Two iterative graph-drawing algorithms that try to minimize the dilation coefficient of a given graph are given. The calculated upper bounds for the dilation coefficients of complete graphs are compared to the values obtained by the graph-drawing algorithms.

Ključne riječi
dilation coefficient; graph representation; energy of a representation; algorithm; circular representation; complete graph; circular packing

Hrčak ID: 45617

URI
https://hrcak.srce.hr/45617

Posjeta: 1.085 *